Identifying overconstraints using port abstraction graphs

ABSTRACT

Overconstraints in a system, such as an electrical circuit layout, are identified using port abstraction graphs. Intercell pitchmatching constraints are represented by meta-edges between cells. Classes of edges which can be represented by a support edge are created, and the value of the class edges are increased to the value of the support edge. The edge values are updated in the graphs, and the redundant edges eliminated. Overconstraints are identified as positive cycles in the graphs, and a database of the layout is annotated and graphically displayed. The graphical display responds to user inputs to manipulate the display of the relations between constraints. The use of the port abstraction graphs also reduces the number of equations that need to be solved to compact the layout.

RELATED APPLICATION

This application is related to the application Ser. No. 07/889,831,filed on May 26, 1992 by Cyrus Bamji and Ravi Varadarajan, entitledHierarchical Pitchmatching Compaction Method and System for IntegratedCircuit Design, which is incorporated by reference herein.

BACKGROUND

1. Field of the Invention

The present invention relates generally to the field of automated designtechniques, and more particularly to methods and systems for identifyingoverconstraints during hierarchical compaction of integrated circuits.

2. Description of the Background Art

Many structures and systems are comprised of components whoseinterrelations are defined by a design rules. Such structures are oftendesigned using automated design techniques employing symbolicrepresentations of the structure and its elements. An example of such astructure is an integrated circuit.

The physical design of an integrated circuit is generally carried out interms of the symbolic layout of the circuit, rather than the actualgeometry of the masks and layers that comprise the chip. When creatingmask works for integrated circuits, designers typically begin with acircuit schematic consisting of an interconnected network of logic orcircuit elements. The designer generally has available a library of maskwork patterns or "cells" which corresponds to the various circuitelement used in the design. Creating a mask work then consists oftransforming the circuit schematic by substituting various cells for theschematic circuit elements in such a way as to efficiently use theavailable mask area. The designer can thus work with transistors, wires,and other primitive components, and groups of these components usingsymbolic representations of these circuit elements. The symbolic layoutprovides a higher level of abstraction than the mask layout, and istherefore easier for the designer to manipulate. The use of a symbolicrepresentation allows the designer to simulate and verify the logicaloperation of the circuit before actual fabrication.

A symbolic layout that contains only primitive symbols, i.e.transistors, wires, capacitors and other physical components, is termeda "leaf cell." The connections between cells are called "ports." Manylayouts contain a large number of groups of components that aresubstantially identical. Such a group may be used to define a cell, andthe description of the layout may then be simplified by treating eachsuch group as an instance of this cell. The cell has its own symbol; forexample it may be represented as a rectangle with various ports forconnecting wires or for abutment with ports of adjacent cells that arerepresented similarly. The components of the overall layout then mayconsist of many cells, and the layout represents their relativeplacement and interconnection. Describing the layout in terms of cellsrather than primitive symbols, further simplifies the designer's task.

Obviously this process of grouping elements and cells may be repeated,so that a symbolic layout can be treated as a hierarchical structurewith multiple levels. Each level is a symbolic layout of various cellsand primitive components. Each such cell is in turn a symbolic layout ofsubcells and primitive components, and this layout defines the nextlower level of the hierarchy. Since there may be more than one type ofcell at any given level, the next lower level may contain severaldifferent branches. The cells at the lowest level are leaf cells sincethey contain no subcells, but only primitive components. Cells at anyother level are "hierarchy cells." The hierarchy can be visualized as aninverted "tree" with branches extending downward, and the lowest leveldepends on the branch in which it is located. In short, the leaf cellsare at the ends of the branches, and the trunk of the tree representsthe symbolic layout of the whole chip, which is often termed the "rootcell." This hierarchical description is a natural and conciserepresentation for large designs.

Once the symbolic layout is designed it is tested to verify its logicalfunctioning. Any defective operation is remediated by design changes andre-verified. Once the design verification is completed, the layout istranslated into a mask layout suitable for the actual fabrication of thechip. The translation maps the symbolic representation of the layoutinto a physical structure that implements the function of the layout.This translation requires additional technical information regarding thefabrication technology, which is stored in a "technology database" andused when the translation is carried out. For example, withsemiconductor chips, the translation specifies the configuration of thephysical structure of the circuit, identifying the precise placement andrelationship of the various layers of semiconductors, insulators,substrates and the like. Using the translated layout, the masks for thecircuit are prepared and the circuit is fabricated. The fabricatedcircuit is tested to verify its functional operation. Changes are madeto the symbolic layout to remediate discrepancies between the intendedand actual operation of the circuit, and a new mask work and chip isfabricated. This design and verify process is repeated until the chipoperates as intended.

The task of integrated circuit design generally includes minimizing thegeometrical size of the total structure. Minimization of size increasescircuit performance by decreasing signal transmission distances.Minimization directly seeks to reduce the space between the physicalelements comprising the circuit, such as traces, contacts betweenlayers, and the like. The minimization process is subject to separationconstraints that ensure that the technical design rules are followed andthe integrity of the circuit is maintained.

Separation constraints generally describe the placement of circuitelements with respect to other circuit elements. There are three basictypes of separation constraints:

1. Lower bound constraints: These are constraints that require, for twocircuit elements A and B, that B is at least X units greater than A.Formally: A+X≦B.

2. Upper bound constraints: These are constraints that require, for twocircuit elements A and B, that B is no more than X units greater than A.Formally: A+X≧B.

3. Equality constraints: These are constraints that require, for twocircuit elements A and B, that A is X units from B. Formally: A+X=B.

The constraints that must be adhered to in minimizing a layout are oftwo types:

1. Constraints inherently present in the layout. These are constraintsthat enforce design rule correctness and preserve the underlying circuitintegrity.

2. Additional constraints required by the user, called user definedconstraints.

Inherent constraints, for example, require certain components of thecircuit to be separated by a minimum distance, and the connectionsbetween different components must be maintained. User definedconstraints may include requiring a cell to be of a minimum size toproperly interface with other components.

The automated process of size minimization is known as compaction. Acompactor is a computer program that operates on the input data of asymbolic layout, and produces a new symbolic layout. This new layoutcorresponds to a design of the minimum size circuit that preserves theintegrity of the original circuit and complies with the design rulerequirements. Compaction minimizes an objective function (generallyrepresenting the size of the layout in one dimension), while satisfyingall constraints in the layout.

In some layouts, the defined constraints cannot all be satisfiedsimultaneously and there is no legal solution to the compaction problem.Such a system is said to be "overconstrained." For example, assume acircuit with elements A, B, and C, and the following constraints:

B is at least 5 units greater than A (A+5≦B);

C is at least 10 units greater than B (B+10≦C);

C is no more than 11 units greater than A (A+11≧C).

This system of separation constraints cannot be satisfied because thefirst two require that A is at least 15 units from C, but the lastrequires that A is no more than 11 units from C. Thus this system isoverconstrained.

Current methods for identifying overconstraints are limited to leafcells, and cannot identify overconstraints in hierarchical layouts.However, overconstraints are likely to be present in many largehierarchical layouts. It would be useful to have a compactor having anefficient method to identify and explain the overconstraints inhierarchical layouts and provide meaningful feedback to the user toeliminate them.

Because circuits can contain a complex hierarchy of cells, compaction ofthe physical structure of the circuit must maintain the logical andphysical relationships between circuit elements in different levels ofthe hierarchy. It is necessary to both compact the organization ofelements within a leaf cell and to maintain the port connectivitybetween abutting cells, termed "pitchmatching," while preserving thehierarchical structure. Given these requirements, the global compactionproblem is formulated as a linear programming problem, which is solvedby the "Revised Simplex Method."

Because the constraint system for hierarchical pitchmatching compactionis solved by linear programming, it is much more difficult to detect thesource of the overconstraints. In contrast to leaf cell compaction,where the overconstraints are localized within a cell, in hierarchicalcompaction overconstraints usually occur due to the complex interactionof cells between and across the levels of hierarchy. Thus it isdesirable to provide a method of displaying to the designer therelations between cells that lead to the overconstraint.

Further, as the number of variables and constraints that must be handledgrows with the size of the hierarchy, the computation time increasesrapidly with the hierarchy size. Hence, the complexity of the method issignificant and the size of the layout that can be dealt with islimited. It is desirable then to provide a method that reduces thenumber of variables and constraints that must be solved to compact thelayout, effectively increasing the size of layouts and complexity thatcan be efficiently designed.

In the discussion that follows the overconstraint system and method willbe directed to the reduction of geometrical areas of an integratedcircuit layout. It should be noted, however, that this method and systemfind useful application in the compaction of circuit board layouts aswell.

SUMMARY

The invention provides a method and a system for identifying andgraphically displaying overconstraints in a layout. A non-heuristicgraph-based method processes a system of equations before they aresolved by linear programming to compact the layout. The system ofequations that describe the hierarchical compaction problem and thatneed to be solved by linear programming can be factored into threeclasses of constraints:

1. Intracell constraints that arise from constraints between shapes anddevices within each of the leaf cells.

2. Intercell constraints that arise from electrical and geometricalinteractions between the leaf cells.

3. Loop constraints that capture the geometric pattern of instances ofcells in the layout.

The invention converts the intracell and intercell constraints ofinstances of each leaf cell into graphical representations called "portabstraction graphs." The port abstraction graphs have vertices forrepresenting the ports, or connections, between cells, and edges forrepresenting the separation constraints imposed on the ports by itsinternal construction. A meta-edge between the vertices of the portabstraction graphs represents the logical relationship between connectedports in different cells or within a cell. The invention identifies andclassifies the edges of the port abstraction graphs and processes theirvalues until individual edges, representing the most significantconstraints between cells, are identified. Redundant edges areeliminated, reducing the number of variables and constraints to processduring compaction. As the edges have signed values representing theseparation constraints, positive and negative cycles are formed alongconnected edges in the port abstraction graphs. Overconstraints aremanifest as positive cycles in the port abstraction graphs, and areannotated in a database. The edges contributing to the overconstraintsare displayed, along with the required spacing constraints between them,letting the designer quickly locate the source of the overconstraints. Adesigner can thus graphically examine the annotated database to pinpointthe cause and location(s) involved in the overconstraint. Identifyingoverconstraints in the leaf cells implicitly identifies overconstraintsin hierarchical cells.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a system for identifying and displayingoverconstraints in a layout;

FIG. 2A is a pictorial illustration of a layout schematic containingcells;

FIG. 2B is a pictorial illustration of three port abstraction graphslinked by meta-edges;

FIG. 2C is a pictorial illustration of three port abstraction graphsfollowing the creation of edge equivalence classes;

FIG. 2D is a pictorial illustration of three updated port abstractiongraphs;

FIG. 2E is a pictorial illustration of a port abstraction graph showinga positive cycle;

FIG. 3 is a flow chart of a method for identifying overconstraints;

FIG. 4 is a flow chart of the process of creating edge equivalenceclasses;

FIG. 5 is a flow chart of the process of annotating a layout database;

FIG. 6A is a pictorial illustration of a computer display screen showinga window for displaying the annotated layout database; and

FIG. 6B is a schematic illustration of the window of FIG. 6A;

FIG. 7 is a pictorial illustration of a computer display screen showinga control window for controlling the display of the annotated layoutdatabase.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to FIG. 1, there is shown a pictorial illustration of asystem for identifying and displaying overconstraints in the layout ofan electrical circuit. The preferred embodiment is implemented on ageneral purpose computer such as a Sun Microsystems, Inc. workstation.Utilizing dedicated software, the general purpose computer specificallyconfigures memory and system peripherals for executing steps of themethod of the present invention.

Overconstraint system 100 comprises processor 11, display 13, massstorage 15, printer 17, keyboard 19, and addressable memory 21.Processor 11 executes method steps stored in, and retrieves and storesinformation to, addressable memory 21. Keyboard 19 and display 13provide a user interface to processor 11. Printer 17 generates apermanent record of the overconstrained circuit component.

Processor 11 is connected to various memories and storage devices inaddressable memory 21 through data bus 35. Connected to data bus 35 areport abstraction graph register 23, edge equivalence class register 25,meta-edge register 27, support edge register 29, and layout database 33.Each of these registers is accessed by processor 11 to obtain and storeinformation according to method steps stored in instruction memory 31.

Layout database 33 contains a coordinate description of a circuit layouthaving a plurality of cells, each cell containing either other cells orcircuit elements. Each circuit element in each cell is identified alongwith its coordinates. Ports, which are the connections between cells arealso identified for each cell. FIG. 2A shows an abstracted schematic ofa layout of circuit elements, showing cells A, B, and C containingvarious AND, NOR gates, and inverters with ports P1-P11 couplingabutting cells. Layout database 33 would contain a description of eachcell sufficient to describe the internal circuit elements, includingtheir ports and positions. Display 13 provides a graphical display ofthe circuit elements stored in layout database 33 following theidentification of overconstraints by the method of the preferredembodiment.

Processor 11 accesses the information stored in layout database 33 tocreate port abstraction graphs of each unique leaf cell in the layout,which are then stored in port abstraction graph register 23. FIG. 2Bshows the port abstraction graphs of cells A, B, and C of FIG. 2A. Ineach port abstraction graph a source vertex S is created and edgesbetween the source vertex S and other vertices are created such that allvertices are reachable along a path from the source vertex S. A sinkvertex E is also created and edges are added to the sink vertex E suchthat the sink vertex E is reachable from any vertex. The connectionsbetween cells A, B, and C are made through ports. In the portabstraction graph for a cell the ports of the cells are represented byvertices. These are shown in FIG. 2B as ports P1, P2, and P3 for cell A,ports P4, P5, and P6 for cell B, and ports P9, P10 and P11 for cell C.

The separation constraints between the ports of a cell become edges in aport abstraction graph. FIG. 2B shows the separation constraints fromthe cells of FIG. 2A as edges E1-E11. These edges have values that arethe spacing requirements induced on the ports by the circuit elements ofthe cell and the circuit designer. Each edge E1-E11 has a direction, asrepresented by the arrow, running from a source port to a sink port.Positive values are minimum separation requirements, and negative valuesare maximum separation requirements, from the source port to the sinkport. Thus in FIG. 2B, in the port abstraction graph of cell A, ports P1and P2 are separated by edge E1 having a value of (10), running fromport P1 to port P2. This means that port P2 (the sink port) must beseparated by at least 10 units from port P1 (the source port).Similarly, in cell C, ports P9 and P11 are separated by edge E11 with avalue of (-15); thus port P9 can be no more than 15 units from port P11.The edge values are the intracell constraints, as described above, andare determined by performing a transitive closure analysis on a leafcell constraint graph, as described in the related application, and inC. Bamji and R. Varadarajan, Hierarchical Pitchmatching Compaction UsingMinimum Design, ACM IEEE 29th Design Automation Conference, 1992. Themethod of the preferred embodiment uses the direction and value of edgesE1-E11 to identify overconstraints in cells A, B, and C.

Processor 11 accesses layout database 33 to identify and storemeta-edges of the port abstraction graphs in meta-edge register 27.Meta-edges M represent pitchmatching constraints between cells sharing agiven interface I. FIG. 2A shows cells A and B sharing interface I(AB).Each interface I gives rise to a set of intercell constraints thatcapture the connection requirements for that interface. Each intercellconstraint is represented by a meta-edge M between the correspondingports of the respective port abstraction graphs of the cells sharing theinterface.

FIG. 2B shows meta-edges M1 through M8 between the port abstractiongraphs of cells A, B, and C. Specifically, cells A and B share interfaceI(AB) (FIG. 2A), and have meta-edges M1, M2, and M3 along that interfacebetween the pairs of corresponding ports (P1, P4), (P2, P5) and (P3,P6), respectively. Similarly, between cells B and C meta-edges M4 and M5couple pairs of ports (P7, P9) and (P8, P11) respectively, acrossinterface I(BC) (FIG. 2A). As FIG. 2A shows, cell A is also coupled tocell C along interface I(AC). Thus the port abstraction graphs of thesecells show meta-edges M6, M7 and M8 between pairs of ports (P1, P9) (P2,P10) and (P3, P11), respectively.

The direction of each meta-edge M is the same as the direction of theinterface between its origin cell and each meta-edge M is labeled in theport abstraction register 23 with the interface I that generates thatconnection. If an interface I is defined from a cell to itself (forexample if cell A were coupled to another cell A), the source and sinkports of the meta-edge M are in the same port abstraction graph (e.g.there would be a meta-edge M looping from port P1 to port P2). Once allthe meta-edges M have been identified, they are stored in meta-edgeregister 27, with indicia of their source and sink ports, and interfacesI.

Processor 11 accesses port abstraction graph register 23 and themeta-edge register 27 to obtain data to identify and store sets ofseparation constraints in edge equivalence class register 25. An edgeequivalence class contains edges E of port abstraction graphs whichshare ports P bound by a pair of meta-edges M along a common interfaceI. Generally, any two edges E of the port abstraction graphs, whosesource and sink ports P are connected together by meta-edges M(A) andM(B) of the same interface I are said to be in the same edge equivalenceclass.

Formally, Edges Ei and Ej in port abstraction graphs are in the sameedge equivalence class, if and only if:

1. The source port of Ei, is connected to the source port of Ej by ameta-edge M(source(i,j));

2. The sink port of Ei is connected to the sink port of Ej by ameta-edge M(sink(i,j)); and

3. M(sink(i,j)) and M(source(i,j)) have the same interface I.

The edge equivalence classes are computed by the union find method of R.E. Tarjan, described in Data Structures and Network Algorithms, SIAM,Philadelphia, Pa., 1986. For every pair of edges E in the portabstraction graphs that meet the criteria of edge equivalence, theirequivalence classes are merged.

Referring now to FIG. 3, there is shown a flow chart of the process 300for identifying overconstraints. As stated above, a layout is comprisedof either leaf cells or hierarchy cells, the former containing primitiveelements, and the latter containing other cells, including leaf cells.Since most circuits are made of repeating cell structures, there arerelatively few unique leaf cells within a layout. Thus instead ofreviewing every cell instance in the layout, it is sufficient to analyzeeach unique leaf cell. For each unique leaf cell then, a portabstraction graph is created 301, and stored in the port abstractiongraph register 23.

Next, the overconstraint process creates 303 meta-edges M from the portabstraction graphs. As there are a relatively small number of uniqueleaf cells, so too are there relatively few unique interfaces I betweencells. Since meta-edges M are bound to the interfaces, each uniqueinterface I is identified in layout database 33. For each uniqueinterface, the ports P coupled to the interface are examined, andmeta-edges M between those ports P are created 303, and stored inmeta-edge register 27.

Once meta-edges M are created for each interface, the edge equivalenceclass are created 305, according to a process shown in FIG. 4. The edgescomprising each equivalence class, as defined above, are stored in edgeequivalence register 25. For the purposes of the discussion of theprocess 300, with respect to FIG. 2C, it suffices to state that the edgeequivalence classes are {E1, E3, E6}, {E2, E4, E7}, {E5, E8, E9, E10},and {E11, E12, E13}. Edges E9 and E10 are new edges created during thecreation 305 of the edge equivalence class to provide correspondingedges to edge E8. Likewise, edges E12, and E13 were new edges created305 to provide corresponding edges to edge E11. The values of E9, E10,E12, and E13 are set to negative infinity. The process of creating 305the edge equivalence classes will be further described below withrespect to FIG. 4.

Following the creation 305 of the edge equivalence classes, process 300then updates 307 each class. Updating 307 replaces the constraint valuesof all the edges E in an equivalence class with the value of a "supportedge" for that class. The support edge of an edge equivalence class isthe edge E representing the strongest separation constraint, that is,the edge E having the largest separation value between the ports P itconnects. The spacing between the pairs of ports P for all edges E in anequivalence class must satisfy the spacing requirements of the supportedge. This is because after hierarchical compaction, the final spacingsbetween the source and sink ports for all edges E in a given equivalenceclass must be the same. Thus the value of all edges E in an equivalenceclass can be increased to the value of the support edge without changingthe results of the final compaction. Updating 307 results in oneequation corresponding to the support edge representing all of the edgesE in its edge equivalence class in the final constraint system to besolved by linear programming, thus minimizing the number of equationsthat need to be solved overall.

An example of updating 307 of the values of edges E is shown in FIG. 2D.Beginning with the values of the edges shown in FIG. 2C, which aredetermined as described above using transitive closure, the edgeequivalence classes contain {E1, E3, E6}, {E2, E4, E7}, {E5, E8, E9,E10}, and {E11, E12, E13}. The support edges of these edge equivalenceclasses are edge E1, E4, E8 and E11, respectively, and these edges arestored in support edge register 29. Update 307 changes the values of theother edges in each of edge equivalence classes to the value of thesupport edge of the class. Thus, the values of edges E3 and E6 are setto (10), the values of edges E2 and E7 are set to (8), the values ofedges E5, E9, and E10 are set to (15), and edges E12 and E13 are set to(-15).

Once the edge equivalence classes are updated 307, the values of someedges E increase to the value of the support edge of the class. This mayresult in an increase in the total separation value along someinterfaces in the port abstraction graphs. For some port abstractiongraphs the value of the longest path from a source port to a sink portmight have increased enough so that it is now greater than (or equal to)the value of edge between those ports. For example in FIG. 2D, the valueof edge E8 (15) is less the value of the path including edges E7 and E6(8+10=18). Such edges are redundant because they do not captureseparation constraints that are not already present along other edges,and are called transitive closure redundant edges.

To determine which edges have become transitive closure redundant theport abstraction graphs are repropagated 309. This process is achievedby running an all pair shortest path algorithm on all the portabstraction graphs; the preferred embodiment uses a modified BellmanFord algorithm. The values of the transitive closure redundant edges arechanged to the value of the longest path between their source and sinkports. Continuing with the above example, FIG. 2E shows the portabstraction graph of cell C, with the value of E8 set to (18).Transitive closure redundant edges are indicated in layout database 33.

After this repropagation 309, some of the edge equivalence classes mightagain need to be updated 307 because the values of the transitiveclosure redundant edges contained in a class will have increased. Thisin turn causes the values of all edges in the class to increase duringthe next update 307 of the edge equivalence class. Following the nextupdate 307, another repropagation 309 of the port abstraction graphsoccurs, wherein still more edges might become transitive closureredundant.

This sequence of alternating between updating 307 the edge equivalentclasses and repropagation 309 of the port abstraction graphs terminateswhen updating the edge equivalence classes does not increase the valueof any edges in that class, or a positive cycle is detected 311following repropagation 309 of a port abstraction graph.

Positive cycles can result from increases in the values of edges E whenthe edge equivalence classes are updated 307. Positive cycles may alsoresult from existing design rules within a cell. Positive cycles areindicative of overconstraints. Accordingly, after repropagation 309,test 311 determines if any positive cycles were formed during the updateprocess. FIG. 2E of cell C following repropagation 309 shows a positivecycle of value (3) along edges E8 (18) and E11 (-15) between ports P9and P11. In other words, edge E8 requires that port P11 be at least 18units from port P9 while edge E11 requires that P9 be no more than 15units from P11. These two separation constraints cannot both besatisfied simultaneously, and thus cell C is overconstrained.

When an overconstraint is detected, layout database 33 is annotated 313with enough information to completely explain the cause of theoverconstraint. The designer can browse 315 through a displayed view ofthe annotated database and discover the cause of the overconstraint.

In order to provide the designer information with which to correct thecause of overconstraints, it is useful to determine whether the edgesinvolved in the overconstraint came to have their values during theupdating 307 of the edge equivalence classes or whether the edge wasmade transitive closure redundant during graph repropagation 309. Thisinformation is created during annotation 313 as follows.

The constraint value on an edge E of a port abstraction graph can bederived from one of the three following categories:

1. The value of an edge E is derived from that of the support edge inits equivalence class. With each such edge E layout database 33 isannotated 313 to identify the support edge of its class.

2. Edge E is a transitive closure redundant edge whose value is derivedfrom the longest path between its source and sink ports P. With eachsuch edge E, layout database 33 is annotated 313 to identify the list ofedges on the longest path between the edge's source and sink port in theport abstraction graph.

3. The value of edge E is derived from the longest path between itssource and sink port, in the complete constraint graph of that cell.Edges whose values are derived from the complete constraint graph can bewithout reference to other edges in the port abstraction graph, butmerely by reference to the underlying edges in the complete constraintgraph. Accordingly, with each such edge, layout database 33 is annotated313 to identify the list of edges on the longest path between its sourceand sink in the complete constraint graph.

FIG. 5 shows a flow chart of annotation process 313. Annotation 313begins by marking 501 in layout database 33 all the edges E involved inthe positive value cycle. Continuing the example of FIG. 2E, edges E8and E11 are marked in layout database 33 to indicate that they create anoverconstraint. After an edge is marked 501 in layout database 33, allassociated edges are also marked 503 and the association relationsbetween them indicated. This means that the edges that provided thevalues to edges in the overconstraint are also marked, and the type ofrelationship between the edges, from those listed above, is indicated.Thus if an edge becomes part of an overconstraint because it was updated307 to the value of the support edge of its edge equivalence class, thenthe support edge is marked 503 in layout database 33, and thisrelationship is indicated. Continuing the example of FIG. 2E, edge E8became transitive closure redundant during repropagation 309 because itsvalue was less than the total separation value of the path along edgesE7 and E6 from port P9 to port P11. Accordingly, edges E7 and E6 aremarked 503 in layout database 33 and the transitive closure redundantrelationship is indicated.

Block 503 causes associated edges and the associated relations to beadded to the annotated layout database 33. The values on these newlyadded associated edges are also explained. The value of each such edgecan in turn be explained by its own set of associated edges. Thisrecursion terminates when an edge in the complete constraint graph ofthe cell is encountered because the value of this type of edge isderived from design rule considerations and is not derived from otherassociated edges. Hence in test 505, when a non "complete constraintgraph" edge is encountered block 503 is performed recursively for eachof the associated edges.

Returning to the example of FIGS. 2D and 2E, edges E7 and E6 wereupdated 307 to their values from the values of the support edges E4 andE1 in their respective edge equivalence classes. Thus edges E4 and E1would be marked 503, and the support edge relationship indicated inlayout database 33. The values of E1 and E4 can be derived from edgesthe complete constraint graph of cell B. These edges in the completeconstraint graph do not depend on other edges in the constraint graph.Rather these edges are separation constraints derived directly fromdesign rules, and are the origin of the overconstraints. The designercan change the design rules producing these separation constraints toremove the overconstraint.

Once layout database 33 is completely annotated 313, it remains toprovide the information about the overconstraints to the designer in auseful manner. An embodiment of the present invention provides a methodfor displaying the annotated layout database 33. FIG. 6A shows apictorial illustration of a layout window 601 on computer display 13,and FIG. 6B shows which of the cells of FIG. 6A are the same in thewindow 601. Window 601 is a mode for translating the information of theport abstraction graphs as annotated 313 in layout database 33 into avisual representation.

Window 601 displays a set of cells 603 forming a portion of a circuitlayout. Cells 603(a) are all identical, as are cells 603(b), and 603(c)respectively. Each cell 603 is comprised of ports 605 and contacts 607.These elements are constrained by separation constraints 615-645, whichare represented by edges E in the port abstraction graphs of a layout.Thus in cell 603(a) in the lower right corner of FIG. 6, port 609 isrelated to port 611 by separation constraint 631; port 611 is related toport 613 by separation constraints 627, 629, and 645, and port 609 isrelated to port 613 by separation constraint 635. The display of window601 is controlled by control window 701 of FIG. 7.

In FIG. 7, control window 701 provides information about separationconstraints, extracting information from annotated layout database 33.Control window 701 further affords a means for manipulating the displayof cells 603 in window 601. Control window 701 displays informationabout an given separation constraint (edge) selected by the designerusing controls 711-725. Controls 711-725 are invoked using conventionalinputs devices such as a mouse or a trackball, touch screen, or thelike. Once a separation constraint is selected, level field 703 isupdated to indicate the level of the selected constraint. The edgesinvolved in the overconstraint cycle are deemed level 1 in level field703; the edges from which their values were derived are level 2, and soon, according to the level of recursion reached during annotation 501 oflayout database 33. Edge value field 705 shows the actual value of theseparation constraint. Edge name field 707 shows the name of theselected edge. Edge type field 709 indicates the type of edge selected,according to the three categories set forth above with respect to FIG.5. The display and function of controls 711-725 is dependent on thecurrent level and element displayed, with only the controls that areapplicable at any given time being displayed in control window 701. Anexample of the use of control window 701 with respect to layout window601 can now be described.

Upon initially invoking layout window 601 for browsing 315 throughlayout database 33, the overconstrained ports containing a positivecycle in a port abstraction graph are highlighted, and the fields ofcontrol window 701 are updated to display the information for one of theseparation constraints in the positive cycle from layout database 33. Inthe example of FIG. 6, the overconstraint arises between ports 609 and613 along separation constraints 631, 635, and 645. Simply put,separation constraints 631 and 645 together require a minimum distancebetween ports 609 and 613 that is greater than the maximum distancespecified by separation constraint 635. Initially, ports 609 and 611 arehighlighted. The designer can then determine which separationconstraints caused the positive cycle by invoking the expand edgecontrol 713 on separation constraint 631. Layout window 601 is thenupdated to show that the value of separation constraint 631 was inducedby separation constraints 633 between contacts 615. One of theseseparation constraints 633 then becomes the selected edge in controlwindow 701, and the fields are updated with information about the value,name, level, and type of that separation constraint.

For example, if the top most separation constraint 633 was selected,then level field 703 would be updated to "2" since this is the secondlevel from the positive cycle. Invoking next control 721 then selectsanother separation constraint from this group and display its associatedinformation. Invoking pop control 715 returns to displaying theinformation for separation constraint 631, and highlighting ports 609and 611. The designer can then examine separation constraints 645 and635 in turn. Invoking next control 721 highlights separation constraint645. Type field 709 indicates that this edge is transitive closureredundant. To learn which constraints made separation constraint 645transitive closure redundant the designer invokes expand control 713 toexpand that edge, thereby highlighting separation constraints 627 and629. Level field 703 now indicates that the level is 2. The display thusindicates to the designer that separation constraint 645 was transitiveclosure redundant because it was less than or equal to the combinedvalue of separation constraints 627 and 629. Invoking current control719 selects one of these separation constraints, namely 627. Type field709 is updated to display "meta edge." The value of this separationconstraint is derived from the support of its edge equivalence class.Invoking support control 723 highlights separation constraint 637 in topright cell 603(d) which is the support of that the edge equivalenceclass of separation constraint 627. Level field 703 is updated todisplay "3", and type field 709 displays "basic edge." Invoking expandcontrol 713 then expands separation constraint 637 into compactorconstraint graph edges 639 and 641. Invoking current control 719 thenhighlights separation constraint 639. Level field 701 is updated to "4"and type field 709 is updated to "compactor edge." This separationconstraint cannot be further expanded (the expand button is removed fromdisplay 701) because its value is derived directly from design ruleconsiderations. Invoking pop control 715 resumes the display ofseparation constraint 637. Level field 703 is decremented to "3", andtype field 709 returns to "basic edge." The process of selecting andexpanding is repeated by the designer until he is satisfied that heunderstands the source of the overconstraint.

Once the designer has identified the cause or causes of anoverconstraint he then accesses layout database 33 to change theseparation values between various circuit elements and then generates anew layout. The layout is then processed for compaction usingconventional methods, and then before actual computation of thecompaction routine, is processed according to method 300 of the presentinvention to identify overconstraints in the new layout.

If no overconstraints remain in the new layout, then for each edgeequivalence class, it now suffices to create only one separationconstraint, the constraint for the support edge of the class. However,the support edge of an edge equivalence class might itself be atransitive closure redundant edge. This is because when the edgesbelonging to the port abstraction graph are updated their combinedvalues exceeds the value of the support. The support edge of theequivalence class is thus subsumed by the constraints imposed by theedges of the port abstraction graph. In this case the constraint carriedby the support edge is already captured by other edges in its portabstraction graph and therefore no constraint is generated. Thissignificantly reduces the number of equations for intracell constraintsthat need to be solved by linear programming.

Following the removal of all overconstraints, there is a minimal set ofequations that define the minimal set of separation constraints forminimizing the layout. These equations are sent 317 to a linearprogramming process for determination of final compacted layout design.

Referring now to FIG. 4, there is shown a flow chart of the process 305for creating edge equivalence classes. First, an edge equivalence classis created 401 for each edge in each port abstraction graph, and storedin edge equivalence class register 25. Next, an iterative loop is begunby selecting 403 a first unique leaf cell in the layout from layoutdatabase 33. As stated above, layouts generally comprise repeatedapplications of a small set of cells. Thus, identifying theoverconstraints in each unique leaf cell is sufficient to analyze theentire layout.

A second iterative loop is begun by selecting 405 from the portabstraction graph register 23 a first edge in the port abstraction graphfor the leaf cell. Next, for the first edge, a first pair of meta-edgeshaving a same interface is identified 407 in the meta-edge register 27.A pair of meta-edges will conform to the requirements set forth abovewith respect to meta-edge register 27. Once a pair of meta-edges for thefirst edge are identified 407, it can then be determined 409 whetherthere is a corresponding edge in a port abstraction graph that sharesthe meta-edges at its sink and source ports. If there is such an edge,then the edge equivalence classes of the two edges are merged 411, andthe results updated to edge equivalence class register 25. If there isno corresponding edge then the first edge is marked 413 in portabstraction graph register 23 to later create 421 corresponding edges inthe port abstraction graphs.

After edge equivalence classes are merged 411 or the first edge marked413, test 415 determines if there is another pair of meta-edges coupledto the first edge. If there is, process 305 loops back to test 409. Ifthere is no other pairs of meta-edges, then test 417 determines whetherthere is another edge in the port abstraction graph of the first cell.If so, then process 305 loops back to select 405 another edge. If not,then test 419 determines whether there remain any unique cells foranalyzing remaining edges. If so, process 305 loops back and selects 403a next unique leaf cell from layout database 33.

If all unique leaf cells have been examined, then for each marked edgein port abstraction graph register 23 a corresponding edge is created421 between source and sink vertices that share the meta-edges of themarked edge. The value of each new edge is set to negative infinity.Once the new edges are created, process 305 terminates and control isreturned to the main process 300.

Referring to FIG. 2B, an example of process 305 can be described asfollows. First, an edge equivalence class is created 401 for each edgein cells A, B, and C. Thus there are initially edge equivalence classes{E1}, {E2}, {E3}, {E4}, {E5}, {E6}, {E7}, {E8} and {E11}.

Next, cell A is selected 403, and a first edge E1 is selected 405. Apair of meta-edges (M1, M2) is identified 407 for edge E1, since thesemeta-edges run from the source and sink ports of edge E1. Acorresponding edge having source and sink ports attached to meta-edgesM1 and M2 is located 409 in the port abstraction graph of cell B at edgeE3. Thus the equivalence classes {E1} and {E3} are merged 411 into {E1,E3}, and edge equivalence register 25 is updated. At test 415 there isanother pair of meta-edges for edge E1, (M6, M7), running between cell Aand cell C. A corresponding edge E6 is located 409 and the edgeequivalence classes {E1, E3} and {E6} are merged 411 into {E1, E3, E6}.

As there is no other pairs of meta-edges for edge E1 at test 415,another edge, edge E2, is selected 405. A pair of meta-edges (M2, M3) isidentified 407 for edge E2, and a corresponding edge E4 is located 409in the port abstraction graph for cell B at edge E4. The equivalenceclasses {E2} and {E4} are merged 411 into {E2, E4}. At test 415 there isanother pair of meta-edges for edge E2, (M7, M8), running between cell Aand cell V. A corresponding edge E7 is located 409 and the edgeequivalence classes {E2, E4} and {E7} are merged 411 into {E2, E4, E7}.Since there are no more meta-edges for edge E2 at test 415, and thereare no more edges in cell A at test 417, the next cell B is selected403.

In cell B, a first edge E3 is selected 405. However, there are no pairsof meta-edges that have not been analyzed for the interface for edge E3.Similarly for edge E4. Edge E5 is then selected 405 and a pair ofmeta-edges (M4, M5) is identified 407. A corresponding edge E8 islocated 409 and the equivalence classes {E5} and {E8} are merged 411into {E5, E8}. These changes are updated to edge equivalence classregister 25. There are no remaining edges in cell B at this point.

Finally, cell C is selected 403, and a first edge E6 is selected 405.This edge has no meta-edges that have not been examined. Similarly withedge E7. When edge E8 is selected 405, meta-edge pair (M8, M6) isidentified 407. As there is no corresponding edge in cell A at test 409,edge E8 is marked 413 to create an edge in cell A. The next edge E11 isselected 405, and meta-edge pair (M8, M6) identified 407. Since there isno corresponding edge cell A, edge E11 is marked 413 for later creationof an edge.

Now all cells have been tested 419, and the marked edges E8 and E11 areexamined 421. For edge E8, edge E9 is created in the port abstractiongraph of cell A between ports P1 and P3 and set to negative infinity;the port abstraction graph of cell A is updated in port abstractiongraph register 23. For edge E11, edge E12 is created in the portabstraction graph of cell A, similarly to edge E9.

Then the port abstraction graph of cell A is reexamined for edge E9, andsince there is meta-edge pair (M1, M3) running to the port abstractiongraph of cell B for ports P4 and P6, an edge E10 is created therebetweenand set to negative infinity. Edge equivalence classes {E5, E8}, {E9}and {E10} are merged.

The port abstraction graph of cell A is reexamined for edge E12, and thedue to meta-edge pair (M1, M3) running to ports P4 and P6, an edge E13is created therebetween and its separation value is set to negativeinfinity. The edge equivalence classes {E11}, {E12} and {E13} are mergedinto {E11, E12, E13}.

At the end of process 305 then, there are edge equivalence classes {E2,E4, E7}, {E1, E3, E6}, {E5, E8, E9, E10} and {E11, E12, E13}. FIG. 2Cshows the results of process 305. Control is then returned to process300.

As describe above, process 300 reduces the number of equationsrepresenting separation constraints that must be solved by linearprogramming during compaction. This allows the creation and compactionof effectively larger layouts. Table 1 shows two examples of thereduction in the number of constraint equations resulting from the useof process 300.

                  TABLE 1                                                         ______________________________________                                                 Number of LP Equations                                               Layout No. With Process 300                                                                           Without Process 300                                   ______________________________________                                        Example 1  350           808                                                  Example 2  711          1908                                                  ______________________________________                                    

Accordingly, the method and apparatus of the present invention provide ameans of identifying overconstraints in the layout of an electricalcircuit, and displaying those overconstraints to a circuit designer. Thepresent invention further minimizes the number of equations necessary tocompact a layout, thereby effectively increasing the size of layoutsthat can be compacted.

While the present invention been described in considerable detail in thepreferred embodiment for identifying overconstraints in circuit layouts,other embodiments of the invention in other uses or environments arepossible. In alternate embodiments, the present invention can be used toidentify overconstraints in many diverse structures or systems thatrequires elements of the structure or system to satisfy rules regardingthe interrelation or position of the elements.

For example, in architectural design, the elements that define thestructure of a building are subject to various design rules that dictatetheir relations with one another, such as rules establishing how closelyone structural element can be placed to another. Thus, an embodiment ofthe present invention could be employed to identify overconstraints inthe structural design, where the design rule overconstraint the place ofvarious architectural elements. Further, an embodiment of the presentinvention could be used to identify overconstraints in the allocation oftime for the performance of a series of tasks, where certain tasks mustbe completed within specific time periods with respect to other tasks.In such a context overconstraints represent a set of timing requirementsthat cannot be satisfied. Thus, in litigation case management wherevarious court rules define the timing of briefs, motions, discoveryrequests, court appearances, the present invention could identifyoverconstraints in an attorney's docket for a case or a set of cases.

Further, the present invention can also be applied in other embodimentsfor reducing the number of equations which define a series of variablesrepresentative of a physical system or structure.

The spirit and scope of the invention is not intended to be limited tothe description of the preferred embodiment herein, but can beimplemented in other environments or combinations, and is capable ofmodification or changes within the details of the inventive conceptdescribed above.

We claim:
 1. In a computer automated design system for designing astructure including a plurality of interconnected cells, in which eachcell includes either another cell or at least one structural element,and each structural element in a cell is related to at least onestructural element in the cell by a constraint with a value, and at sleast one structural element in each cell is interconnected to astructural element in another cell, a computer implemented method foridentifying overconstraints in the structure prior to completing thestructure, comprising the steps of:creating a plurality of constraintsets, each constraint set consisting of constraints that will have asame value in the completed structure by:generating a graph of each cellincluding only structural elements, in which a structural element of acell is represented as a vertex, and a constraint between two structuralelements is represented by an edge coupling a pair of verticesrepresenting the structural elements, the edge having a length equal tothe value of the constraint; adding a pair of meta-edges between pairsof corresponding vertices in at least two graphs, where a first vertexand a second vertex in a first graph corresponds to a third vertex and afourth vertex in a second graph where:a first structural element in afirst cell represented by the first vertex is interconnected with athird structural element in a second cell represented by the thirdvertex; a second structural element in the first cell represented by thesecond vertex is interconnected with a fourth structural element in thesecond cell; there is a first constraint between the first and secondstructural elements, and a second constraint between the third andfourth structural elements, the first constraint represented by a firstedge in the first graph, and the second constraint represented by asecond edge in the second graph; and, generating at least one edgeequivalence class each edge equivalence class containing all edges ofthe graphs whose vertices are coupled by pairs of meta-edges; updatingeach of the plurality of constraint sets so that each constraint in aconstraint set has the value of the constraint in the set having agreatest value; and, identifying in a cell a set of interconnectedstructural elements having constraints with a net positive value for allconstraints in the set, the positive cycle identifying an overconstrainton the interconnected structural elements.
 2. The method of claim 1,wherein the step of updating the sets of constraints, further comprisesthe steps of:updating the edges in the edge equivalence classes bysetting the length of each edge in an edge equivalence class to thelength of an edge having a greatest length; and repropagating the graphof each cell to remove each edge having a length equal to or less than alongest distance between the vertices coupled to the edge.
 3. The methodof claim 2, wherein the step of identifying in a cell a set ofinterconnected structural elements having constraints with a netpositive value for all constraints in the set, further comprises thestep of:detecting at least one positive cycle within a graph, thepositive cycle identifying an overconstraint for a set of edges of thegraph.
 4. A method for displaying overconstrained ports in a layoutcircuit represented by a plurality of cells, each cell having portsseparated by constraints, each constraint having a value, where thevalues of constraints in selected cells are induced by constraints inother cells, comprising the steps of:displaying a plurality of cells ona display; displaying the ports of each displayed cell; determining atleast one port in at least one first cell that is overconstrained as aresult of constraints between the first cell and selected other cells;highlighting in a displayed cell the at least one port that isoverconstrained; displaying a value of a first constraint for thehighlighted port on the display; determining at least one secondconstraint in either the first cell or the selected other cells thatinduced the first constraint; and highlighting in a displayed cell thesecond constraint.
 5. In a computer automated design environment fordesigning structures, a computer implemented method for identifyingoverconstraints in a s structure including a plurality of interconnectedstructural elements, and a plurality of cells, in which each cellincludes either a structural element or a cell, and each cell hasconnections to at least one other cell made by connection points, and adistance between connections, the method comprising the stepsof:generating a graph of each cell in the structure, in which eachconnection point is represented as vertex, and the distances betweenconnection points within a same cell are represented by edges havinglengths equal to the distances between the connection points; adding apair of meta-edges between pairs of vertices in graphs, each meta-edgerepresenting connections between the connection points of cells; isgenerating at least one edge equivalence class, each edge equivalenceclass containing all edges of the graphs whose vertices are coupled bypairs of meta-edges; updating the edges in the edge equivalence classesby setting the length of each edge in an edge equivalence class to thelength of the edge having the greatest length; repropagating the graphsof the cells to remove each edge having a length equal to or less than alongest distance between the vertices coupled to the edge; and detectingat least one positive cycle within a graph, the positive cycleidentifying an overconstraint for a set of edges of the graph.
 6. In acomputer automated design environment for designing a plurality ofinterconnected electrical systems, where each electrical system haselectrical elements, and selected first electrical elements in a firstelectrical system are interconnected with selected second electricalelements in a second electrical system, such that the first and secondelectrical elements have interrelated constraints realized byparametersh, and the constraints have relations to constraints in otherelectrical systems, a computer implemented method for identifying theconstraints in each electrical system that are induced by constraints inother electrical systems, comprising the steps:a) creating a pluralityof constraint equivalence sets, each set containing constraints whichmust be realized by a same parameter by:for each relation between afirst constraint in a first electrical system and a second constraint ina second electrical system, creating a meta-constraint associated withthe first and second constraints; for each constraint in each electricalsystem, creating a constraint equivalence set including the constraint;and, merging a first constraint equivalence set and a second constraintequivalence set where a first constraint in the first constraintequivalence set and a second constraint in the second constraintequivalence set are associated with a pair of same meta-constraints; b)for each constraint equivalence set, resetting each constraint in theconstraint equivalence set to a most stringent constraint in thatconstraint equivalence set; c) for each electrical system, propagatingeach reset constraint in the electrical system to satisfy itsinterrelated constraints; and d) repeating steps b) and c) until noconstraint is reset in step b) where for each constraint equivalenceset, the most stringent constraint in the constraint equivalence set isthe constraint that induced the other constraints in that constraintequivalence set.
 7. A computer implemented method for identifyingoverconstraints in a circuit including a plurality of interconnectedcircuit elements, and a plurality of cells, in which each cell includeseither a circuit element or a cell, and each cell has connections to atleast one other cell made by connection points, and a distance betweenthe connections, the method comprising the steps of:generating a graphof each cell in the circuit, in which the connection points arerepresented as vertices, and the distances between connection pointswithin a same cell are represented by edges having lengths equal to thedistances between the connection points; adding meta-edges between pairsof vertices in graphs, each meta-edge representing connections betweenthe connection points of cells; generating edge equivalence classes foreach edge in each graph, each edge equivalence class containing alledges of the graphs whose vertices are coupled by pairs of meta-edges;updating the edges in the edge equivalence classes by setting the lengthof each edge in an edge equivalence class to the length of the edgehaving the greatest length; repropagating the graphs of the cells toremove edges having a length equal to or less than a longest distancebetween the vertices coupled to the edge; and detecting at least onepositive cycle within a graph, the positive cycle identifying anoverconstraint for a set of edges of the graph.
 8. A computerimplemented method for determining the identity of overconstraints in anelectrical circuit during hierarchical compaction, the electricalcircuit represented symbolically having a plurality of cells, each cellrepresented by a port abstraction graph wherein ports within cells arerepresented as vertices, and separation constraints on the ports arerepresented by edges having values, and two cells abut each other alongan interface, the method comprising the steps of:identifying each pairof vertices in either the same or different port abstraction graphs forwhich there is an intercell constraint between the ports represented bythe vertices; adding a meta-edge between each pair of vertices, eachmeta-edge associated with an interface; generating at least one edgeequivalence class, each edge equivalence class containing all edges ofthe port abstraction graphs whose vertices are coupled by meta-edges ofa same interface; updating the port abstraction graphs so that each edgein each port abstraction graph has the value of the edge in its edgeequivalence class having a greatest value; and, detecting whether thereexists a positive cycle within at least one port abstraction graph, thepositive cycle identifying the edges of the port abstraction graphcontributing to the overconstraint in the electrical circuit.
 9. Themethod of claim 8, wherein the step of updating the port abstractiongraphs, further comprises the steps of:updating the edges in each edgeequivalence classes by setting the edge value of each edge in an edgeequivalence class to the value of the edge in the class having agreatest value; and repropagating the port abstraction graphs of thecells to remove transitive closure redundant edges.
 10. The method ofclaim 9, further comprising the step of:annotating a database containinga description of the electrical circuit to indicate the edgescontributing to the overconstraint.
 11. The method of claim 9, furthercomprising the steps of:displaying the cells represented by the portabstraction graphs on a computer display; highlighting in the displayedcells circuit elements corresponding to overconstrained ports; anddisplaying the values of separation constraints for the highlightedcircuit elements.
 12. The method of claim 11, further comprising thesteps of:receiving at least one user input selecting at least onecircuit element corresponding to an overconstrained port; and,recursively highlighting in the displayed cells the circuit elementsthat contributed to the overconstrained ports in response to the userinputs, and displaying the separation constraints for the displayedcircuit elements.
 13. For an electrical circuit including a plurality ofinterconnected cells, in which each cell includes either another cell orat least one circuit element, and each circuit element in a cell isrelated to at least one circuit element in the cell by a constraint witha value, and at least one circuit element in each cell is interconnectedto a circuit element in another cell, a computer implemented method foridentifying overconstraints in a completed circuit, comprising the stepsof:creating a plurality of constraint sets, each constraint setconsisting of constraints that will have a same value in the completedcircuit by:generating a graph of each cell including only circuitelements, in which a circuit element of a cell is represented as avertex, and a constraint of a circuit element is represented by an edgecoupling a pair of vertices, the edge having a length equal to the valueof the constraint; adding a meta-edge between pairs of correspondingvertices in at least two graphs; and, generating edge equivalenceclasses for each edge in each graph, each edge equivalence classcontaining all edges of the graphs whose vertices are coupled by pairsof meta-edges; updating each of the plurality of constraint sets so thateach constraint in a constraint set has the value of the constraint inthe set having a greatest value; and, identifying in a cell a set ofinterconnected circuit elements having constraints with a net positivevalue for all constraints in the set.
 14. The method of claim 13,wherein the step of updating the sets of constraints, further comprisesthe steps of:updating the edges in the edge equivalence classes bysetting the length of each edge in an edge equivalence class to thelength of an edge having a greatest length; and repropagating the graphsof each cell to remove edges having a length equal to or less than alongest distance between the vertices coupled to the edge.
 15. Themethod of claim 14, wherein the step of identifying in a cell a set ofinterconnected circuit elements having constraints with a net positivevalue for all constraints in the set, further comprises the stepof:detecting at least one positive cycle within a graph, the positivecycle identifying an overconstraint for a set of edges of the graph.